Continuity and discontinuity of deﬁnite properties in the modal interpretation
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Technical results about the time dependence of eigenvectors of reduced density operators are considered, and the relevance of these results is discussed for modal interpretations of quantum mechanics which take the corresponding eigenprojections to represent deﬁnite properties. Continuous eigenvectors can be found if degeneracies are avoided. We show that, in ﬁnite dimensions, the space of degenerate operators has co-dimension 3 in the space of all reduced operators, suggesting that continuous eigenvectors almost surely exist. In any dimension, even when degeneracies are hit, we ﬁnd conditions under which a theorem due to Rellich can provide continuous eigenvectors. We use this result to formulate an extended version of the modal interpretation. We also discuss eigenvector instability which we argue poses a serious problem for the modal interpretation, even in our extended version. Many examples are given to illustrate the mathematics.
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Citations of this work BETA
Dennis Dieks (2007). Probability in Modal Interpretations of Quantum Mechanics. Studies in History and Philosophy of Science Part B 38 (2):292-310.
Guido Bacciagaluppi & Meir Hemmo (1996). Modal Interpretations, Decoherence and Measurements. Studies in History and Philosophy of Science Part B 27 (3):239-277.
Dennis Dieks (2007). Probability in Modal Interpretations of Quantum Mechanics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):292-310.
Guido Bacciagaluppi & Meir Hemmo (1996). Modal Interpretations, Decoherence and Measurements. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 27 (3):239-277.
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